Lyot filters are widely used to obtain spectral filters of narrow bandpass. They are made of a stack of filter stages, each stage having a fixed retarder plate placed between linear polarizers. Although several variations have been developed, the basic design uses a single retarder per stage, with its slow axis oriented at 45 degrees to the entrance polarizer axis; the exit polarizer of each stage is oriented parallel to the entrance polarizer. The effect is that the stage passes light of wavelength .lambda..sub.0 =R/n without loss, where R is the retardance of the retarder plate and n is an integer. The wavelength .lambda..sub.0 which satisfies this equation for a given n is termed the passband center for the order n, and in general several orders may be present. The spacing between successive transmission peaks is termed the free spectral range (FSR), and for n&gt;&gt;1 is approximated by ##EQU1##
The wavelength separation between the points on the filter transmission curve where the transmission curve falls to half of its peak value is termed the full-width at half-maximum (FWHM); for one of these stages the FWHM is half its free spectral range, or ##EQU2##
In the simplest case, a filter consists of several of these stages in series, where each stage has a retarder twice as thick as the previous one In this way the unwanted transmission peaks of the i+1 stage align with the transmission minima of the i-th stage, and so are extinguished. On the other hand, the passband width of the i+1 element is half that of the i-th stage, as given by the above equation. By stacking several elements in series, a very narrow passband can be obtained while maintaining a wide free spectral range. The ultimate bandwidth limit can be quite narrow (0.020 nm) if retarders of high order are employed.
It is common to use `wide-field` retarder elements for the thickest few elements. These are composed of two retarders of half the desired thickness, separated by a half-wave plate. The half-wave plate is oriented with its fast axis at 45 degrees from the fast axis of the first retarder, and the second retarder is oriented at 90 degrees. This produces the same retardance as a single element for on-axis rays, but its retardance is less sensitive to variations in incidence angle. This increases the field of view of the resulting filter.
Various schemes have been devised to permit tuning of the filter passband; the most widely used places achromatic quarter-wave retarders in series with rotating polarizers or achromatic half-wave retarders. These schemes require mechanical rotation of such elements by hand or by servo-motor in order to effect tuning. Since one element must be adjusted for each stage, the resulting systems are mechanically complex.
Other tuning schemes have employed potassium dihydrogen phosphate (KDP) or other electro-optic tuning elements to directly adjust the retardance. However, these materials require high voltages (&gt;2 kV) to achieve tuning, and are plagued with electrode decay and other operating problems.
Liquid crystals may be used as the retarder medium if they exhibit a nematic phase. In this phase, individual molecules can move freely like molecules in a liquid, but they posess an overall orientation like molecules in a crystal. Because the molecules exhibit retardance, which can be altered by an applied electric field, they may be used as variable retarders. These materials may be used as the retarder elements in Lyot filters [Kaye, 1983] where they are operated with order n of 1 to 15. Single elements can be used to realize excellent rejection at a single wavelength, and Kaye [1985] describes how to make a notch rejection filter which is operated in sequence at a variety of orders, to realize a high average transmission at the transmitted wavelengths, when time-averaged.
To realize high spectral resolvance, it is necessary to have some method of accurately controlling the retardance of each element. This is difficult when using liquid crystal elements: first, the liquid crystal material properties are sensitive to temperature; and second, the retardance of such a cell depends on voltage in a complicated, non-linear way. Finally, it is difficult to construct high order (narrowband) filters, as it is not possible to make liquid crystal retarders with extreme uniformity or high R. For example, Lyot filters used in solar astronomy require that the retarders operate with order n of 10,000 or more. Such elements could not be built using liquid crystals alone.
Improved nematic retarder elements have been described by researchers who have increased their response speed [Fergason, Bos] and off-axis response [Kaye, 1984]. Active retardance sensing and servo systems have been described [Miller] which overcome the thermal and device-to-device variations of these elements and render them suitable for use in precision optical systems. However, such sensing systems have always required one optical sensor per liquid crystal element, and require that a portion of the cell be dedicated to monitoring the retardance. This decreases the useful cell aperture and adds cost and complexity, particularly when many liquid crystal elements are used.
Present cells also are limited in their versatility since thick liquid crystal cells are slow in response and exhibit substantial off-axis retardance variations. The thick cells are needed when there is a larger amount of retardance required, yet they have poorly controlled retardance. Cell life is also a problem with DC-driven thick cells.
Accurate control of any liquid crystal variable retardance cells is also difficult since the response of the cells is not linear to the drive voltage. Some method of sensing and correcting the retardance is required.
There is a need for a variable retarder that is fast in switching time, easily controllable without need for constant optical measurements, and that will permit lower costs of complex retarder systems.
It would also be an advantage if the retarder systems could be switched rapidly and reliably between defined levels of retardance for the purpose of difference or ratio comparisons. This would be useful in instruments in many fields.
Retarder systems are now expensive due to the test and calibration needed for each system. It would be an advantage to have systems that are made with lower cost elements, and to remove some of the expensive calibration and characterization without adding additional steps to the manufacture.
These needs at present are not met by existing retarders or use expensive or complex systems.